Nonparametric Estimation for a General Repair Model.
FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS
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The construction and analysis of repair models is an important area in reliability. A commonly used model is the minimal repair model. Under this model, repair restores the state of the system to its level prior to failure. Kijima introduced repair models that could be classified as better-than-minimal. Under Kijimas models, the system, upon repair, is functionally the same as a working system of lesser age which has never experienced failure. In this paper, we present a new approach to the modelling of better-than-minimal repair models. Using this approach, we construct a general repair model that contains Kijimas models as special cases. We also study the problem of estimating the distribution of the time to first failure of a system maintained by general repair. We make use of counting processes to show strong consistency of the estimator and prove results on weak convergence. Finally, we derive a Hall-Wellner type asymptotic confidence band for the estimator.
- Statistics and Probability